(a) Using your favorite method, find the potential V{r) everywhere as a function of r, with V = U at innity. (b) For a collection of point charges: the total potential energy is U0 =_ =_ , ,- Lt 2; w 2:; :qu where the factor of 1/ 2 is to correct for double counting. For a continuous charge distri- bution such as our charged spherical shell, the analogous expression is 1 Umt = if V{I') d9 where (it; is an infinitesimal bit of charge located at position r. Use the potential you found in (a) to find Una in terms of a and q (the radius of the sphere and its total charge, respectively) as well as any necessary constants